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Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

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  • Dominik Łuczak

    (Faculty of Automatic Control, Robotics and Electrical Engineering, Poznan University of Technology, 60-965 Poznań, Poland)

Abstract

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.

Suggested Citation

  • Dominik Łuczak, 2021. "Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part," Energies, MDPI, vol. 14(21), pages 1-12, November.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:21:p:7190-:d:670327
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    References listed on IDEAS

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    1. Krzysztof Szabat & Karol Wróbel & Krzysztof Dróżdż & Dariusz Janiszewski & Tomasz Pajchrowski & Adrian Wójcik, 2020. "A Fuzzy Unscented Kalman Filter in the Adaptive Control System of a Drive System with a Flexible Joint," Energies, MDPI, vol. 13(8), pages 1-18, April.
    2. Radosław Nalepa & Karol Najdek & Karol Wróbel & Krzysztof Szabat, 2020. "Application of D-Decomposition Technique to Selection of Controller Parameters for a Two-Mass Drive System," Energies, MDPI, vol. 13(24), pages 1-21, December.
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    Cited by:

    1. Karol Wróbel & Kacper Śleszycki & Krzysztof Szabat & Seiichiro Katsura, 2021. "Application of Multilayer Observer for a Drive System with Flexibility," Energies, MDPI, vol. 14(24), pages 1-19, December.
    2. Karol Wróbel & Kacper Śleszycki & Amanuel Haftu Kahsay & Krzysztof Szabat & Seiichiro Katsura, 2023. "Robust Speed Control of Uncertain Two-Mass System," Energies, MDPI, vol. 16(17), pages 1-17, August.
    3. Piotr Derugo & Krzysztof Szabat & Tomasz Pajchrowski & Krzysztof Zawirski, 2022. "Fuzzy Adaptive Type II Controller for Two-Mass System," Energies, MDPI, vol. 15(2), pages 1-24, January.
    4. Krzysztof Szabat & Tomasz Pajchrowski & Tomasz Tarczewski, 2021. "Modern Electrical Drives: Trends, Problems, and Challenges," Energies, MDPI, vol. 15(1), pages 1-4, December.

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